The energy bills of 11m households will be capped for as long as five years under legislation put forward by government, which the Conservatives have claimed could save people up to £100 a year.

The draft energy bill compels regulator Ofgem to change the licence conditions for energy suppliers so that they are forced to cap electricity and gas prices.

The measure will apply to anyone on a standard variable tariff, the expensive plans that customers are moved to when cheaper, fixed deals end.

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Analysts believe the cap is unlikely to take effect until the start of 2019 at the earliest, because of the legislative process. It will be in place until at least the end of 2020, but Ofgem will be able to extend it until the end of 2023, if competition is not deemed to be working.

The draft legislation published on Thursday does not spell out at what price the average dual fuel bill will be capped.

By comparison, the average standard variable tariff offered by the big six suppliers is £1,142, so the wider cap is likely to be below that and above £1,031.

Ofgem will need to consult energy companies on how the cap is calculated, the government said.

Ministers confirmed that Ofgem would be compelled to implement the cap once the law had given it new powers. Labour had previously raised doubts as to whether the legislation would force Ofgem to act, or simply empower it.

The draft legislation also reveals that the cap will be an absolute one. A relative cap, for which some MPs have been pushing and which would limit a supplier’s most expensive tariff to a percentage above their cheapest deal, has been ruled out.

“I have been clear that our broken energy market has to change – it has to offer fairer prices for millions of loyal customers who have been paying hundreds of pounds too much,” said May.

“Today’s publication of draft legislation is a vital step towards fixing that, and in offering crucial peace of mind for ordinary working families all over the country.”

Share prices in SSE, one of the UK’s biggest energy companies, were up by 1.76%, while British Gas owner Centrica climbed 2.6%. Hundreds of millions of pounds have been wiped off the firms’ market value since May announced the cap in her Conservative party conference speech.

Citizens Advice, a charity which has a statutory duty to protect energy customers, welcomed the government’s move to legislate.

Gillian Guy, the Citizens Advice chief executive, said: “The runaway costs of default energy tariffs need to be tackled, and this draft bill is an important step towards an energy market that works better for consumers.”

However, Which?, a consumer organisation which was enthusiastic about the limited cap for 1 million people, said ministers needed to be careful the wider one did not backfire.

Alex Neill, the group’s managing director of home products and services, said: “For millions of consumers worried about their energy bills, a cap might sound like a positive move. However, the government must guard against any unintended consequences that undermine customer service and push up prices as a whole.”

One comparison site strongly condemned the government for pushing ahead with a wide-ranging cap.

Richard Neudegg, head of regulation at uSwitch.com, said: “The proposal for a widespread price cap verges on negligence by the government. They are sending out completely the wrong message by suggesting that a price cap will improve the retail energy market.”

The Liberal Democrat MP and former energy minister, Ed Davey, said competition would be harmed and prices would climb up to the cap. The Lib Dems were the only main political party to oppose price caps during the last election.

One of the big six suppliers was critical of the government pushing ahead with a broad cap.

Michael Lewis, chief executive of E.ON, said: “A price cap will not be good for customers. It will reduce engagement, dampen competition and innovation.”

However, smaller suppliers such as First Utility said the big six had only themselves to blame for the cap, because they had kept millions of people on standard variable tariffs.